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Simplifying 3x2 + 180x + 200 = 0 Reorder the terms: 200 + 180x + 3x2 = 0 Solving 200 + 180x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 66.66666667 + 60x + x2 = 0 Move the constant term to the right: Add '-66.66666667' to each side of the equation. 66.66666667 + 60x + -66.66666667 + x2 = 0 + -66.66666667 Reorder the terms: 66.66666667 + -66.66666667 + 60x + x2 = 0 + -66.66666667 Combine like terms: 66.66666667 + -66.66666667 = 0.00000000 0.00000000 + 60x + x2 = 0 + -66.66666667 60x + x2 = 0 + -66.66666667 Combine like terms: 0 + -66.66666667 = -66.66666667 60x + x2 = -66.66666667 The x term is 60x. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60x + 900 + x2 = -66.66666667 + 900 Reorder the terms: 900 + 60x + x2 = -66.66666667 + 900 Combine like terms: -66.66666667 + 900 = 833.33333333 900 + 60x + x2 = 833.33333333 Factor a perfect square on the left side: (x + 30)(x + 30) = 833.33333333 Calculate the square root of the right side: 28.867513459 Break this problem into two subproblems by setting (x + 30) equal to 28.867513459 and -28.867513459.Subproblem 1
x + 30 = 28.867513459 Simplifying x + 30 = 28.867513459 Reorder the terms: 30 + x = 28.867513459 Solving 30 + x = 28.867513459 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 28.867513459 + -30 Combine like terms: 30 + -30 = 0 0 + x = 28.867513459 + -30 x = 28.867513459 + -30 Combine like terms: 28.867513459 + -30 = -1.132486541 x = -1.132486541 Simplifying x = -1.132486541Subproblem 2
x + 30 = -28.867513459 Simplifying x + 30 = -28.867513459 Reorder the terms: 30 + x = -28.867513459 Solving 30 + x = -28.867513459 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = -28.867513459 + -30 Combine like terms: 30 + -30 = 0 0 + x = -28.867513459 + -30 x = -28.867513459 + -30 Combine like terms: -28.867513459 + -30 = -58.867513459 x = -58.867513459 Simplifying x = -58.867513459Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.132486541, -58.867513459}
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